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# If you can solve this I will give you a million dollars

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If you can solve this I will give you a million dollars Jul 27, 2020

#1
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Is this an AoPS question?

Jul 27, 2020
#2
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Since AQ is an angle bisector, angle CAQ is 45 degrees.  We are told that angle PAQ is 13 degrees, so angle RAC is 45 + 13 = 58 degrees.

Jul 27, 2020
#5
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you don't get a million dollars if you get it wrong

qwertyzz  Jul 27, 2020
#3
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oops this was wrong

Jul 27, 2020
edited by Sub2JessieGamez  Jul 27, 2020
#4
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you don't get a million dollars if you get it wrong

qwertyzz  Jul 27, 2020
#6
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Wait you wont give the person who solves this one million dollars i bet :p

Jul 27, 2020
#7
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I have only 68 dollars sooo

qwertyzz  Jul 27, 2020
#8
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I'll give you the answer but you have to solve it. ∠BAP = ∠ACB = ∠RAC = arctan( AB / AC ) Jul 27, 2020
edited by Dragan  Jul 27, 2020
edited by Dragan  Jul 27, 2020
#9
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Assuming that P, Q, and R are on BC (in the order B, P, Q, R, C):

Angle(BAC) = 90.

Since AQ is an angle bisector, angle(BAQ) = 45.

Since P is between B and Q and angle(PAQ) = 13, angle(BAP) = angle(BAQ) - angle(PAQ)

--->   angle(BAP) = 45 - 13 = 32.

Since AP is an altitude, angle(BPA) = 90.

In triangle(BAP), angle(BAP) = 32 and angle(BPA) = 90   --->   angle(ABP) = 58.

In triangle(BAC), angle(BAC) = 90 and angle(ABP) = 58   --->   angle(ACB) = 32.

Since AR is a median of a right triangle, RA = RB = RC.

Since RA = RC, triangle(ARC) is an isosceles triangle.

Since angle(ACB) = 32, ange(CAR) = 32.

Jul 28, 2020
#10
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Ok here is a million dollars :P

\$1,000,000

qwertyzz  Jul 28, 2020